Enter an equation
Use one equals sign and the variable x. The answer will appear here.
Recent calculation history
History stays in this browser and can reload earlier equations.
Formula used
Linear equations use inverse operations. Quadratic equations use factoring, completing the square, or the quadratic formula.
Linear: ax + b = 0 → x = −b/a Quadratic: ax² + bx + c = 0 → x = (−b ± √(b² − 4ac)) / 2a Absolute value: |u| = k → u = k or u = −k Radical: √u = k → u = k², then verify Exponential: aᵘ = b → u = logₐ(b) Logarithmic: logₐ(u) = b → u = aᵇ
How to use this calculator
Enter one equation containing x. Use one equals sign and balanced parentheses.
Select a preferred answer format. Choose the graph range and decimal precision.
Press Solve for x. Review every step and verify carefully.
Example equations
| Equation | Type | Expected answer | Action |
|---|---|---|---|
3x + 5 = 20 |
Linear | 5 | |
2(x - 4) = 3x + 1 |
Variables on both sides | -9 | |
x^2 - 5x + 6 = 0 |
Quadratic | 2, 3 | |
|2x - 3| = 7 |
Absolute value | -2, 5 | |
sqrt(3x + 1) = 4 |
Radical | 5 | |
2^(x + 1) = 16 |
Exponential | 3 | |
log10(x) = 2 |
Logarithmic | 100 | |
4x + 8 = 4(x + 2) |
Identity | All real numbers |
Important algebra terms
Equation: A statement showing two expressions have equal values.
Variable: A symbol representing an unknown or changing value.
Coefficient: A number multiplying a variable, such as 3 in 3x.
Root: A value making an equation or polynomial equal zero.
Solution set: Every value that satisfies the original equation.
Frequently asked questions
What does solving for x mean?
It means finding every x value that makes the equation true.
Can the calculator solve variables on both sides?
Yes. It moves terms, combines like terms, and isolates x.
Does it solve quadratic equations?
Yes. It handles real, repeated, and complex quadratic roots.
Can I enter fractions?
Yes. Use division notation such as x/3 or (x+1)/4.
How are answers verified?
The calculator substitutes solutions into the original equation when supported.
Why can an equation have no solution?
Simplification may produce a contradiction or violate a function domain.
What does infinitely many solutions mean?
Both sides simplify identically, so every real x works.
What is an extraneous solution?
It appears during algebra but fails the original equation check.
Which equation forms are restricted?
General cubic, trigonometric, and variable-denominator equations need specialised symbolic software.